69.22.14 problem 719

Internal problem ID [18480]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 719
Date solved : Thursday, October 02, 2025 at 03:14:09 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ y \left (1\right )&=0 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 12

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-diff(y(x),x)-y(x) = 0; 
ic:=[y(0) = -1, y(1) = 0, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (-1+x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 14

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-D[y[x],x]-y[x]==0; 
ic={y[0]==-1,y[1]==0,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} (x-1) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): -1, y(1): 0, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (x - 1\right ) e^{- x} \]